The Anthropic Principles – Reasonable and Unreasonable

and the fallacy of
the abduction-type inference to a supernatural source of the big bang

by Mark
Perakh

First
posted on August 10, 2000. Updated July 30, 2001.

This article is not a detailed discussion of the multitude of questions
related to the anthropic principle. There is a vast literature devoted to
such discussions, where the anthropic principle has been analyzed in great
detail and from various viewpoints. This article offers a very simple and to a
certain extent superficial discussion of the anthropic principle in Bayesian
probabilistic terms. While it simplifies the problem under discussion, it
is offered with an intention to demonstrate that certain interpretations
of anthropic principle can easily be refuted based on quite simple
probabilistic grounds.

The term anthropic principle
apparently started gaining popularity after 1973, when an English physicist,
Brandon Carter introduced it at a gathering of scientists on the occasion of the
500th anniversary of Copernicus's birth. Carter noted that the values of physical
constants must be within a very narrow range in order to enable the existence of
life, and that the observed values of those constants happen indeed to be in
that narrow range. In other words, the universe appears to be "fine-tuned" for
the existence of life. Were any of
the physical constants slightly different, life would be impossible.

Since then, the anthropic principle, as Carter's observation was labeled,
has become a favorite subject of discussion by many adherents of the Bible's
inerrancy, who view it as a convincing proof that the universe, as we see it,
and intelligent life in particular, could not emerge by chance but must have
been created for a purpose and according to a detailed design by a supernatural
agent.

For example, Hugh Ross has extensively written about the anthropic
principle, listing multiple examples of physical constants whose values seem to
be very finely tuned for the existence of life (as in his article [1]). Professor Nathan Aviezer also argued [2]
in favor of the above supernatural interpretation of the anthropic principle.
Similar discussions can be found in many other publications by the proponents of
the supernatural creation of the universe and life, such as books by Fred Heeren
[3] or Patrick Glynn [4], a paper by Walter L. Bradley [5] and many other
publications.

Of course, those adherents of such view, who approach it from a
Christian perspective, interpret it differently from those who are believing
Jews. For the former, the anthropic principle points to Jesus Christ as the
creator of the universe, whereas for the latter Jesus has nothing to do with the
creation of the world by Yahve (Jehovah). It is easy to see that if we accept the thesis that anthropic principle
indeed proves that the universe was created by a supernatural agent, it still
leaves many variations of that explanation equally possible. Without contradicting the mentioned
general interpretation of the anthropic principle, one can equally guess that
the creator of the world was either the biblical Yahve or Quetzalcoatl, or
Krishna, or Jupiter, or a band of smaller gods all working in cahoots.

However, in this article I will try to show that the above interpretation
is unsubstantiated in general, regardless of the particular choice of a
candidate for the role of the supernatural Creator of the world. I will try to show that if the universe
is indeed fine-tuned for life this
does not logically point to the supernatural creation of the world and of life,
such an interpretation being just one of many possible, equally arbitrary
assumptions.

First, let us note that after Carter's introduction of the concept
of the anthropic principle, a number of versions of the latter have been
offered. One such version is often
referred to as the Weak Anthropic Principle (WAP). For example, here is how the famous
physicist Stephen Hawking defines the WAP in his popular book A Brief History
of Time[6]: "The weak anthropic principle states that in a universe that is
large or infinite in space and/or in time, the conditions necessary for the
development of intelligent life will be met only in certain regions that are
limited in space and time. The intelligent beings in these regions should
therefore not be surprised if they observe that their locality in the universe
satisfies the conditions that are necessary for their existence." From that definition we see that the WAP
does not require the assumption of a supernatural agent being responsible for
the creation of the universe and of life.

Another version of the anthropic principle is often referred to as
the Strong Anthropic Principle (SAP). Here is how Hawking defines the latter:
"According to this theory, there are either many different universes, or many
different regions of a single universe, each with its own initial configuration
and, perhaps, with its own set of laws of science. In most of these universes
the conditions would not be right for the development of complicated organisms;
only in the few universes that are like ours would intelligent life develop and
ask the question, 'Why is the universe the way we see it?' The answer is simple: if it had
been different, we would not be here." We see that the SAP itself does
not necessarily imply the supernatural creation of the universe either.

One more version of the anthropic principle was offered [7] under
the name of the Participatory Anthropic Principle. This version made use of the concepts of
quantum mechanics in their so-called "Copenhagen interpretation." This version implies that the very
existence of the universe can only be understood within the framework of an intelligent mind observing the
universe.

Then, there is also the so called Final Anthropic principle [7] which
goes even further, positing that the very existence of the universe is due to
the human mind observing it. Reviewing all described versions of the anthropic principle, Martin
Gardner [8] suggested an all-embracing derogatory term "CRAP, the Completely
Ridiculous Anthropic principle."

While one can be skeptical in regard to the mentioned esoteric
interpretations of Carter's observation of the values of physical constants, the
very fact of their being seemingly "fine-tuned" for the existence of life has
been rather commonly accepted. The
question is, though, what is the meaning of that apparent hospitality of the
universe for the existence of life. Depending on the preferred answer to that
question, we can see a clear
demarcation between two opposite interpretations of the mentioned "fine-tuning."
One interpretation perceives in the fine-tuning of the physical constants an
indication of the creation of the universe by a supernatural agent (God or gods)
for a purpose and according to a plan. The opposite interpretation looks for a
natural explanation of the fact that the universe seems to be fine-tuned for
life.

I suggest to denote all versions of the anthropic principle that
imply only a natural origin of life in our universe, as the Natural Anthropic
Principle (NAP) and all those versions that imply a supernatural creator or
creators, as the Supernatural Anthropic Principle (SNAP).

My further discourse will be of probabilistic nature. I will
estimate what the probability is that the fine-tuning of the universe for life
indicates a supernatural creation of the universe vs. the probability that the universe
had no supernatural creator.

A few words
about the terminology are in order. The adherents of SNAP often discuss the problem in terms of "what if the
physical constants were different." For example, if the value of the strong force were slightly less than it
is in our universe, many atomic nuclei would not exist, so that the only element
in such a universe would be hydrogen, and, hence there would be no life. On the other hand, in a universe where
the strong forces were slightly stronger than in our universe, all hydrogen
would be replaced with helium at an early stage of that universe's formation, so
the stars as we know them would not exist, and therefore there would be no
life. Whereas some theories have
been suggested in which the actual existence of alternative universes have
indeed been postulated, in many discussions hypothetical alternative universes
with different values of physical constants are imagined only for the sake of
discussion. Most often the adherents of SNAP do not assert that indeed such
alternative universes exist or even could exist. Likewise, in my probabilistic discourse,
I will use similar references to
"alternative universes," not implying that such alternative universes really
exist or even may exist.

Before
turning to the probabilistic presentation of the anthropic principle, let me
make a brief excursion into some seminal concepts of the probability
theory.

Let
p(A&B) be the probability that two events A and B both take place. The probability theory tells us that if
A and B are independent events, then

p(A&B) = p(A)×p(B)..........(1)

This equation is often viewed as
the definition of the events' independence.

However, if
A and B are not independent, i.e., if the occurrence of A changes the
probability of B, then we have instead of (1):

p(A&B) = p(A)×p(B|A)..........(2)

where p(A) is the probability of
event A, and p(B|A) is the conditional probability of event B provided event A
takes place. This relation is
pretty self-evident and sometimes is viewed as the definition of the conditional
probability p(B|A).

Likewise, we can
write

p(B&A)= p(B)×p(A|B)..........(3)

Since, obviously, A and B are
arbitrary notations, which may be swapped, we can write:

p(A&B)= p(B&A)..........(4)

which, comparing (2) and (3),
yields:

p(A)×p(B|A)= p(B)×p(A|B)..........(5)

From (5) we get a universal
relation

p(A|B)/p(A)= p(B|A)/p(B)..........(6)

Our equation (6) could have
simply been presented as a consequence of Bayes's theorem, well known in the
probability theory [9]. Alternatively, Bayes's theorem can be easily derived
from equation (6). For this discussion, we will limit ourselves to the
particular, simplified form of Bayes's theorem presented as equation
(6).

It is easy
now to succinctly represent any version of the anthropic principle in
probabilistic terms. For example,
for NAP and SNAP it can be done as follows:

1) NAP:

Let p(FT) be
the probability that a certain universe is fine-tuned for life. Let p(FT|L) be the conditional
probability that a universe is fine-tuned for life provided life exists in that
universe. Let p(L) be the
probability that life exists in a universe, and p(L|FT) the conditional
probability that life exists in a universe provided that that universe is
fine-tuned for life. The equation (6) of probability theory becomes:

p(FT|L)/p(FT) = p(L|FT)/p(L)..........(7)

The Natural Anthropic Principle then boils
down to the statement that

NAP: p(FT|L)» p(FT)..........(8)

The meaning of (8) – the
probabilistic representation of the Natural Anthropic Principle - is the
assertion that the existence of life in a universe makes it much more probable
that the universe in question must be fine-tuned for life (as compared with a
universe where there is no life).

From (7) then follows that
also

p(L|FT)» p(L)..........(9)

The meaning of (9) is that if a
universe is fine-tuned for life, this considerably enhances the probability that
life will exist in that universe (as compared with a universe which is not
fine-tuned for life). This is a
reasonable assumption (some readers may even view it as obvious). If (9) holds, (8) holds as well. Hence,
NAP seems to be a reasonable and logically faultless assumption.

2) SNAP (Supernatural Anthropic Principle). This interpretation of the
anthropic principle is based on the assertion that the existence of life in our
universe is best explained by assuming that the universe was intentionally
"fine-tuned" by a supernatural intelligent agent. In probabilistic terms, this
position can be expressed by the following inequality:

p(S|FT)» p(S)..........(10a)

where p(S) is the probability of
a supernatural creation of the universe and p(S|FT) is the probability of a
supernatural creation provided the universe in question is fine-tuned for
life. Expression (10a) states that the fine-tuning of our universe makes
much more probable its supernatural origin as compared with a universe which
is not "fine-tuned" for life.

According to the proponents of SNAP, life would be impossible
without the "fine-tuning." Therefore, the conditional probability p(S|FT) in the expression (10a)
may be replaced by p(S|L) which is the conditional probability that our
"fine-tuned" universe was created by a supernatural agent, provided life exists
in that universe (as compared with a universe where there is no life).

Then, in
probabilistic terms, SNAP can be rendered by the following
expression:

p(S|L)/p(S) » 1..........(10b)

where p(S) is the probability
that a universe was created supernaturally, and p(S|L) is the conditional
probability that a universe was supernaturally created provided life exists in
that universe.

The relation
(6) is for this case as follows:

p(S|L)/p(S) = p(L|S)/p(L)..........(11)

where p(L|S) is the conditional
probability that life exists in a universe provided that universe was created
supernaturally. To satisfy (10) and
(11) we must assume that

p(L|S)»p(L)..........(12)

The meaning
of (12) is that if we know that a universe was created supernaturally, this
knowledge increases the probability p(L|S) of life's existence in such a
universe compared to the probability p(L) of life's existence in the absence of
knowledge of supernatural creation. This means the assumption that the supernatural creator of a universe
must also have necessarily wished to have created life in it. This is an arbitrary assumption, since
we have no knowledge of what a supernatural creator of a universe may have
wished or not wished to do. Hence SNAP, i.e. expressions (10a) and (10b) also
are arbitrary assumptions. Hence
the Supernatural Anthropic Principle is logically unsubstantiated and is an
arbitrary assumption.

The conclusion that the universe which is fine-tuned for life implies a
supernatural creator is an example of "circular reasoning." In order to conclude
that p(S|L)»p(S) which is a succinct representation of the SNAP, we must first
assume that p(L|S)»p(L), i.e. assume a priori the existence of a supernatural
agent who wished and planned to create life. But the latter assertion is exactly
what was to be proven by the entire discourse.

Of course,
establishing the arbitrariness of an assumption does not mean that such an
assumption is necessarily wrong. It does mean, though, that one may not assert
that such an assumption is correct. At best, the question about the correctness of such an assumption remains
open until some convincing proofs of its being either correct or not are
found. As the matter stands now, no
such proofs have been suggested, so the assertion that the values of physical constants point to the
supernatural origin of the universe and life remains an unsubstantiated
assumption, reflecting religious preferences rather than factual
evidence.

The above
simple probabilistic discourse has shown that the supernatural interpretation of
the anthropic principle, so popular among proponents of creationism, both of
explicit and implicit kinds, is logically unsubstantiated. A further investigation of the logic of
that proposition such, for example, as
that by Michael Ikeda and Bill Jefferys (see The Anthropic Principle Does Not Support Supernaturalism) of
which I did not yet know when first
writing the above discussion, and which is based on the full form of Bayes's
theorem, has provided an even stronger refutation of the hypothesis of a
supernatural creation of life. That
discourse seems to have shown that the more "fine-tuned" for life a universe is,
the less likely is its supernatural origin.

The above discussion can be applied, with a slight modification, to the
discussion of a logical procedure known as "abduction." William A. Dembski and
Stephen C. Meyer provide [10] an explanation of the abduction procedure which
differs in some respects from that concept as it is normally used in both
philosophy of science and in artificial intelligence. Since this
discussion is about Dembski & Meyer's use of that procedure in their attempt
to prove the divine source of the big bang, I will not delve into the
differences between their interpretation of abduction and that which is more
commonly adopted but will rather discuss their paper adopting their definition
of abduction.

Deduction is
a process wherein a certain event A is believed to have actually happened.
If some other event B is an inevitable consequence of A (we say in that case
that A entails B), we infer from the occurrence of A that B necessarily must
occur as well. Dembski and Meyer [10] present the deduction procedure in the
following form:

Data: A is
given and plainly true.
Logic:
But if A is true than B is a matter of course.

Conclusion:
Hence, B must be true as well.

On the other
hand, according to Dembski and Meyer, abduction is a way of inference in certain
respects opposite to deduction. Here is how Dembski and Meyer present the
abduction procedure:

Data: The
surprising fact A is observed
Logic:
But if B were true, then A would be a matter of course

Conclusion:
Hence, there is a reason to suspect that B is true.

It seems
obvious that the inference in the first case is very strong and the conclusion
is as certain as it possibly can be. However, in the second case, the
inference is only tentative -- it only indicates the possibility of B being
true. Indeed, while if B were true, A would be a matter of course, it does not
mean that there are no other C, D, E, etc, which would entail A as well, and
therefore the occurrence of A (the consequent) does not define the antecedent as
being necessarily B, but only indicates that B is one of the possible
antecedents.

Despite the
relative weakness of inference by a way of abduction (in Dembski-Meyer sense),
it is often resorted to as the only available path to a conclusion.
However, if and when abduction has been utilized, one has to be aware of the
tentative character of the conclusion which, if it is expected to be accepted as
true, requires additional supporting evidence.

One of the examples of an unsubstantiated utilization of abduction is the
inference of the supernatural origin of the big bang. In particular, such
an inference is offered in the article [10] by Dembski and Meyer. In his book
"The Design Inference" [11] Dembski turns several times to Bayes's theorem,
showing familiarity with that version of a probabilistic analysis. However, in
his paper [10] with Meyer, Dembski seems to have forgotten about Bayes's
theorem, which is quite relevant to the discussion of the abduction-type
inference. Actually, Bayes's theorem formulates the abduction inference
(in Dembski-Meyer's sense) in probabilistic terms.

Let p(S) be
again the probability that there is a supernatural agent responsible for the
creation of the universe. Let p(S|BB) be the probability of the existence of
that supernatural agent provided the big bang has indeed occurred. Let, further,
p(BB) be the probability of the big bang's occurrence, and p(BB|S) be the
conditional probability of the big bang's occurrence provided there is a
supernatural agent responsible for the creation of the universe. Then our particular, simplified version
of Bayes's theorem - equation (6) - takes the form:

p(S|BB)/p(S)= p(BB|S)/p(BB)..........(13)

The
abduction inference, according to Dembski-Meyer's schema, if presented using the
above version of Bayes's
theorem, can be as follows:

Since,
as they maintain, there exists no good explanation entailing any natural cause
of the big bang, then in their view the hypothesis of a supernatural agent being
the source of the big bang is a better explanation. Hence, if the big bang
occurred, this enhances the probability of a supernatural agent being its
source:

p(S|BB)» P(S)..........(14)

Note that
(14) renders Dembski/Meyer's conclusion of their abduction argument in
probabilistic terms.

In
accordance with (13), if (14) holds, then also

p(BB|S)» p(BB)..........(15)

In plain
words, equation (15) means the assertion that the existence of a supernatural
creator substantially enhances the probability of the occurrence of the big
bang. This equation renders the "logic" step of Dembski/Meyer's abduction
inference in probabilistic form. (The "data" step of their abduction argument is
the assumption that the big bang had actually occurred.) Hence, according to
Dembski-Meyer's abduction inference, if we assume that the big bang had actually
occurred, there is a good reason to assume that a supernatural agent does exist,
which is expressed by inequality (14).

The fallacy
of that inference is in the inequality (15) - p(BB|S)» p(BB). This assumption asserts that the
probability of the actual occurrence of the big bang is substantially enhanced
if there is a supernatural creator of the universe. In terms of the abduction
inference, it means that if a supernatural agent responsible for the creation of
the universe does exist, the big bang is a matter of course. Obviously this is
an arbitrary assumption because we have no knowledge about how a supernatural
agent might act. If (15) is an
arbitrary assumption, so is the conclusion - inequality (14).

Of course,
again, the arbitrariness of the above assumption does not prove that it is
wrong. However, it shows the lack of substantiation for Dembski-Meyer's
hypothesis of a supernatural origin of the big bang, which is only one of many
possible explanations. It has no advantage over any other explanation, including
those denying supernatural creation.